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Abstract: The frequently used approach to the comparison of two linear regression models is to use the partial F test. It is pointed out in this paper that the partial F test has in fact a naturally associated two-sided simultaneous confidence band, which is much more informative than the test itself. But this confidence band is over the entire range of all the covariates. As regression models are true or of interest often only over a restricted region of the covariates, the part of this confidence band outside this region is therefore useless and to ensure simultaneous coverage probability is therefore wasteful of resources. It is proposed that a narrower and hence more efficient confidence band over a restricted region of the covariates should be used. The critical constant required in the construction of this confidence band can be calculated by Monte Carlo simulation. While this two-sided confidence band is suitable for two-sided comparisons of two linear regression models, a more efficient one-sided confidence band can be constructed in a similar way if one is only interested in assessing whether the mean response of one regression model is higher (or lower) than that of the other in the region. The methodologies are illustrated with two examples. [Copyright &y& Elsevier]

Research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means. Several years ago, Spurrier considered the multiple comparison of several simple linear regression lines. He constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range (-∞, ∞) when the models have the same design matrices. This article extends Spurrier's work in several directions. First, multiple linear regression models are considered and the design matrices are allowed to be different. Second, the predictor variables are either unconstrained or constrained to finite intervals. Third, the types of comparison allowed can be very flexible, including pairwise, many-one, and successive. Two simulation methods are proposed for the calculation of critical constants. The methodologies are illustrated with examples. [ABSTRACT FROM AUTHOR]

This paper introduces practical methods of parameter and standard error estimation for adaptive robust regression where errors are assumed to be from a normal/independent family of distributions. In particular, generalized EM algorithms (GEM) are considered for the two cases of t and slash families of distributions. For the t family, one step method is proposed to estimate the degree of freedom parameter. Use of empirical information is suggested for standard error estimation. It is shown that this choice leads to standard errors that can be obtained as a by-product of the GEM algorithm. The proposed methods, as discussed, can be implemented in most available nonlinear regression programs. Details of implementation in SAS NLIN are given using two specific examples. [ABSTRACT FROM AUTHOR]